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  2. If and only if - Wikipedia

    en.wikipedia.org/wiki/If_and_only_if

    The corresponding logical symbols are "", "", [6] and , [10] and sometimes "iff".These are usually treated as equivalent. However, some texts of mathematical logic (particularly those on first-order logic, rather than propositional logic) make a distinction between these, in which the first, ↔, is used as a symbol in logic formulas, while ⇔ is used in reasoning about those logic formulas ...

  3. Logical biconditional - Wikipedia

    en.wikipedia.org/wiki/Logical_biconditional

    Venn diagram of (true part in red) In logic and mathematics, the logical biconditional, also known as material biconditional or equivalence or biimplication or bientailment, is the logical connective used to conjoin two statements and to form the statement "if and only if" (often abbreviated as "iff " [1]), where is known as the antecedent, and the consequent.

  4. English conditional sentences - Wikipedia

    en.wikipedia.org/wiki/English_conditional_sentences

    In English conditional sentences, the antecedent (protasis) is a dependent clause, most commonly introduced by the complementizer if.Other complementizers may also be used, such as whenever, unless, provided (that), and as long as.

  5. Conditional sentence - Wikipedia

    en.wikipedia.org/wiki/Conditional_sentence

    A conditional sentence is a sentence in a natural language that expresses that one thing is contingent on another, e.g., "If it rains, the picnic will be cancelled." They are so called because the impact of the sentence’s main clause is conditional on a subordinate clause.

  6. Logical conjunction - Wikipedia

    en.wikipedia.org/wiki/Logical_conjunction

    The and of a set of operands is true if and only if all of its operands are true, i.e., is true if and only if is true and is true. An operand of a conjunction is a conjunct. [3] Beyond logic, the term "conjunction" also refers to similar concepts in other fields:

  7. Counterfactual conditional - Wikipedia

    en.wikipedia.org/wiki/Counterfactual_conditional

    Moreover, languages that do use the subjunctive for such conditionals only do so if they have a specific past subjunctive form. Thus, subjunctive marking is neither necessary nor sufficient for membership in this class of conditionals. [12] [13] [9] The terms counterfactual and subjunctive have sometimes been repurposed for more specific uses ...

  8. Logical consequence - Wikipedia

    en.wikipedia.org/wiki/Logical_consequence

    A sentence is said to be a logical consequence of a set of sentences, for a given language, if and only if, using only logic (i.e., without regard to any personal interpretations of the sentences) the sentence must be true if every sentence in the set is true.

  9. Logical equivalence - Wikipedia

    en.wikipedia.org/wiki/Logical_equivalence

    This statement expresses the idea "' if and only if '". In particular, the truth value of p ↔ q {\displaystyle p\leftrightarrow q} can change from one model to another. On the other hand, the claim that two formulas are logically equivalent is a statement in metalanguage , which expresses a relationship between two statements p {\displaystyle ...